Answer :

To divide the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex], you follow these steps:

1. Find the reciprocal of the divisor (the second fraction). The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].

2. Multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{13}{15} \times \frac{10}{7}
\][/tex]

3. Multiply the numerators and the denominators of the fractions:
[tex]\[
\text{Numerator: } 13 \times 10 = 130
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 7 = 105
\][/tex]

So the result of the multiplication is [tex]\(\frac{130}{105}\)[/tex].

4. Simplify the fraction [tex]\(\frac{130}{105}\)[/tex] by finding the greatest common divisor (GCD) of 130 and 105. The GCD is 5.

5. Divide the numerator and denominator by their GCD to simplify:
[tex]\[
\text{Simplified Numerator: } \frac{130}{5} = 26
\][/tex]
[tex]\[
\text{Simplified Denominator: } \frac{105}{5} = 21
\][/tex]

Therefore, the simplified form of [tex]\(\frac{130}{105}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex].

Finally, [tex]\(\frac{13}{15} \div \frac{7}{10} = \frac{26}{21}\)[/tex] when written in simplest form.

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